JAMB UTME - Physics - 2017

Calculate the light of the image formed by a pinhole camera of length 12cm used to photograph an object 60cm away from the hole and 70cm high

Bayanin Amsa

Magnification = $\frac{\text{Length of camera}}{\text{distance of object from pin hole}}$

m = $\frac{12}{60}$

= 0.2

Also magnification m = $\frac{\text{Height of image}}{\text{Height of object}}$

∴ Height of image = m × height of object

= 0.2 × 70

= 14cm

It is known that a neutron exists in a light atomic nucleus

Which of the following also exists in the nucleus?

Bayanin Amsa

A neutron is a subatomic particle that has no electric charge and is found in the nucleus of an atom along with protons. Therefore, the correct option is: - proton An electron is a negatively charged subatomic particle that orbits around the nucleus of an atom. A β- particle, also known as a beta particle, is an electron or a positron emitted during radioactive decay. Both of these particles are not found in the nucleus of an atom. On the other hand, a proton is a positively charged subatomic particle that is also found in the nucleus of an atom along with neutrons. The number of protons in the nucleus determines the atomic number of the element. Hence, a proton also exists in the nucleus along with a neutron. In summary, the only subatomic particle that exists in the nucleus along with a neutron is a proton.

From the diagram above, calculate the total current in the circuit

Bayanin Amsa

V = IR from ohms law

I = $\frac{V}{R}$

Since the resistance are in parallel

$\frac{1}{Reff}$ = $\frac{1}{8}$ + $\frac{1}{12}$ + $\frac{1}{6}$

= $\frac{2+3+6}{36}$ = $\frac{11}{36}$

Reff = $\frac{36}{11}$ = 3.27

I = I1 + I2 + I3

= $\frac{V}{Reff}$= $\frac{12}{3.27}$

= 3.669A

I = 3.7A

What is the speed of a body vibrating at 50 cyclic per second

Bayanin Amsa

1 cycle = 3600 = 2? rad

? 50 cycle = 2 ? rad × 50 = 100 ?rad

? = angular speed = 50 cycles per seconds = 100 ? rads${}_{?1}$

The thermal expansion of a solid is an advantage in

Bayanin Amsa

Thermal expansion of a solid is majorly advantageous in the use of bimetallic strip in the balance of a watch so as not to lose time

From the diagram above, calculate the energy stored in the capacitor

Bayanin Amsa

c = 8µF, v = 10v

Energy stored = $\frac{1}{2}$ cv2

= $\frac{1}{2}$ × (8 × 10− 6) × 102

= 4 × 10${}^{-4}$

Which of the following representations is correct for an atom X with 28 electrons and 30 neutrons?

Bayanin Amsa

An atom can be represented thus,

${}_A^{Z}X$ where Z = mass number

A = atomic number

A = number of proton = number of electrons in a free state = 28

Z = number of protons + number of neutrons = 28 + 30 = 58

${}_{28}^{58}X$is the representation

How can energy loss be minimized through Eddy-current?

Bayanin Amsa

Eddy currents are produced by the varying flux cathode, the iron core of an equipment thus reducing efficiency due to power consumption. It can be reduced by laminating the core by breaking up the path of eddy current or by increasing the resistance of the core
Usage of insulated soft iron wire is to reduce hysteresis loss
Usage of low resistance wire (thick wire) is to reduce I2R loss
Usage of thick wire is to reduce leakage heat loss due to leakage of magnetic flux
Thus the correct answer is to use high resistance wire or thin wire

Which of the following operations can be used to convert an alternative current dynamo into a direct current dynamo

Bayanin Amsa

A d.c generator is one in which its current is allowed to flow in one direction even through it may vary in value an a.c generator can only be made to produce a d.c by replacing the two slip rings with a single split ring or commutator.

A block and tackle pulley arrangement has 6 pulleys in which an effort of 50N supports a load of 200N, calculate the efficiency of the machine

Bayanin Amsa

Which of the following is not a mechanical wave?

Bayanin Amsa

Radio waves are not a mechanical wave. Mechanical waves are waves that require a medium to propagate, meaning they can only travel through a physical material. Examples of mechanical waves include sound waves, water waves, and waves in a closed pipe. Radio waves, on the other hand, are electromagnetic waves and do not require a medium to propagate. They can travel through a vacuum, such as space, and are used for communication technologies like radio and television broadcasting, cell phone signals, and GPS.

The instrument used to measure the pressure of a gas is

Bayanin Amsa

Barometer is used to measure atmosphere pressure
Thermometer is used to measure temperature
Hygrometer is used to measure relative density of a liquid
Manometer is used to measure the pressure of a gas

Which of the following is a scalar quantity?

Bayanin Amsa

Scalar quantity is a quantity with only magnitude, it has no direction
Tension, weight, impulse are vector quantities because they have direction. Mass is the only scalar quantity there

A cell of internal resistance 2 π supplies current to a 6 π resistor. The efficiency of the cell is

Bayanin Amsa

Internal resistance determine the maximum current that can be supplied

Efficiency = $\frac{r}{R}$ × 100

= $\text{frca}26$ × 100

= 33.3%

When two mirrors are placed at an angle of 900 to each other, how many images will be formed when an object is placed in front of the mirrors

Bayanin Amsa

When two mirror are inclined at an angle θ, the number of images formed, n = $\frac{360}{\theta }$ − 1

∴ since $\theta$ = 90o

∴ $\frac{360}{\theta }$ − 1

= 4 − 1

= 3

Calculate the angle of minimum deviation of a 60o prism of a refractive index [sin-10.75 = 49o]

Bayanin Amsa

For a refractive index () = $\frac{\sin \frac{1}{2}(A+D)}{\sin \frac{1}{2}A}$

D = angle of minimum deviation

A = refractive angle of the prism

1.5 = $\frac{\sin \frac{1}{2}(60+D)}{\sin \frac{1}{2}\times 60}$

1.5 = $\frac{\sin \frac{1}{2}(60+D)}{\sin 30}$

Sin $\frac{1}{2}$ (60 + D) = 1.5 * Sin 30

Sin $\frac{1}{2}$ (60 + D) = 0.75

$\frac{1}{2}$ (60 + D) = Sin-1 (0.75)

but Sin-1 (0.75) = 49o

$\frac{1}{2}$ (60 + D) = 49

60 + D = 2 * 49 = 98o

D = 98o - 60o

D = 38o

Which of the following is a semiconductor

Bayanin Amsa

The semiconductor among the given options is "silicon." Semiconductors are materials that have electrical conductivity between that of a conductor and an insulator. They are widely used in electronics, such as in the construction of computer chips. Copper is a good conductor of electricity and is commonly used in electrical wiring. It is not a semiconductor. Silicon, on the other hand, is one of the most commonly used semiconductor materials in the electronics industry. It has four valence electrons, which allow it to form a crystal lattice structure with other silicon atoms. This structure gives silicon its unique electrical properties that make it useful in electronic devices such as transistors and solar cells. Plastic and iron are not semiconductors. Plastic is an insulator, which means it does not conduct electricity at all, while iron is a conductor, like copper, and does not exhibit the unique electrical properties of a semiconductor.

The action of blotting paper on ink is due to

Bayanin Amsa

The action of blotting paper on ink is due to capillarity. Capillarity is the ability of a liquid to flow in narrow spaces, such as the fibers of a piece of blotting paper, against the force of gravity. This is made possible because of the combination of the liquid's surface tension, which acts like a skin on the surface of the liquid, and the wicking action of the fibers in the paper. The fibers in the blotting paper wick the ink from the surface it is on, and the ink is held in the fibers due to the surface tension of the liquid. This is why blotting paper is effective in removing excess ink from surfaces, because it pulls the ink into its fibers and holds it there.

The net capacitance in the circuit above is

Bayanin Amsa

For capacitance i n parallel, 2µF and 2µF are in parallel,
their equivalence is 2µF and 2µF = 4µF

The 4µF generated is now in series with the remaining 4µF.

The net capacitance for series connection is

$\frac{1}{C}$ = $\frac{1}{4}$ + $\frac{1}{4}$ = 1 + $\frac{1}{4}$ = $\frac{2}{4}$

C = $\frac{4}{2}$

= 2µF

The instrument to measure the relative density of light is

Bayanin Amsa

The instrument used to measure the relative density of light is a hydrometer. A hydrometer is a device that is designed to measure the density of a liquid by comparing it to the density of water. In order to measure the relative density of light, the hydrometer is placed in a liquid with a known density, such as water. The hydrometer will float at a certain level in the liquid, which indicates the density of the liquid. When measuring the relative density of light, the hydrometer is placed in a liquid that has been made less dense by the addition of a solute, such as sugar or salt. The hydrometer will float at a higher level in the less dense liquid, indicating that the relative density of the light is lower than that of the liquid without the solute. In summary, a hydrometer is the instrument used to measure the relative density of light by comparing it to the density of a liquid with a known density, such as water.

Determine the focal length of a thin converging lens if the power is 5.0 dioptres

Bayanin Amsa

The formula for calculating the focal length (f) of a thin converging lens in meters using its power (P) in dioptres is: f = 1/P In this problem, the power of the lens is given as 5.0 dioptres. So, substituting this value in the above formula, we get: f = 1/5.0 = 0.2 meters Therefore, the focal length of the lens is 0.2 meters (or 20 centimeters). This means that when parallel light rays pass through this lens, they will converge to a point that is 0.2 meters (20 centimeters) away from the lens. The smaller the focal length of a lens, the greater its ability to converge light, and the stronger its power. So, the correct answer is 0.2 m.

Which is the incorrect formula for a body accelerating uniformly?

Bayanin Amsa

s = $\frac{1}{2}$ut + at2 is a wrong equation, it should be s = ut + $\frac{1}{2}$at2

A radio station broadcast at a frequency of 600KHZ. If the speed of light in air is 3 × 108ms${}^{-1}$. Calculate the wavelength of the radio wave

Bayanin Amsa

The formula to calculate the wavelength of a wave is: wavelength = speed of light / frequency where wavelength is the distance between two consecutive peaks or troughs of a wave, frequency is the number of cycles of the wave per second, and the speed of light in air is approximately 3 × 10^8 m/s. In this question, the frequency of the radio wave is given as 600 kHz, which means that it has 600,000 cycles per second. Substituting these values into the formula, we get: wavelength = 3 × 10^8 m/s / 600,000 s^-1 wavelength = 500 m Therefore, the wavelength of the radio wave is 500 meters. The answer is: 5.0 × 10^2 m.

What is the cost of running seven 40 W lamps and five 80 W la mps for 12 hours of the electrical energy cost N7.00kWk?

Bayanin Amsa

To calculate the cost of running the lamps, we need to determine the total energy consumed in kilowatt-hours (kWh) and multiply it by the cost of electrical energy per kWh. First, let's calculate the total power consumption of the lamps: Total power consumption = (7 x 40 W) + (5 x 80 W) = 280 W + 400 W = 680 W Next, let's convert the power consumption to kWh: Energy consumption = (680 W / 1000) x 12 hours = 8.16 kWh Finally, let's calculate the cost of running the lamps: Cost = Energy consumption x Cost of electrical energy per kWh Cost = 8.16 kWh x N7.00/kWh = N57.12 Therefore, the cost of running seven 40 W lamps and five 80 W lamps for 12 hours at an electrical energy cost of N7.00/kWh is N57.12. The correct answer is option D.

An element and its isotope only differ in the number of

Bayanin Amsa

An element and its isotope only differ in the number of neutrons. Isotopes are different forms of the same element that have the same number of protons in their nucleus, but a different number of neutrons. The number of protons determines the identity of the element and is called the atomic number, while the number of neutrons in the nucleus is called the mass number. Therefore, the difference between an element and its isotope is only the number of neutrons, not the number of protons or electrons. The number of protons and electrons are the same for all isotopes of a given element.

Which of the following is not an electromagnetic radiation?

Bayanin Amsa

The answer is: sound waves is not an electromagnetic radiation. Electromagnetic radiation is a type of energy that travels through space at the speed of light in the form of waves. It is made up of oscillating electric and magnetic fields, and it includes a wide range of phenomena such as radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, x-rays, and gamma rays. Sound waves, on the other hand, are not electromagnetic radiation. They are mechanical waves that require a medium to travel through, such as air, water, or solids. When an object vibrates, it creates sound waves that travel through the medium and can be heard by our ears. So, while x-rays, radio waves, and sunlight are all examples of electromagnetic radiation, sound waves are not.

Three 3ω resistance are connected in parallel what is the equivalent resistance?

Bayanin Amsa

Resistor connected in a parallel have an equivalence given by
$\frac{1}{\text{Reff}}$ = $\frac{1}{3}$ + $\frac{1}{3}$ + $\frac{1}{3}$

= $\frac{1+1+1}{3}$ = $\frac{3}{3}$ = 1

Reff = 1ω

Which of the following instruments helps to maintain the correct humidity and temperature of a building?

Bayanin Amsa

The instrument that helps to maintain the correct humidity and temperature of a building is an air conditioner. An air conditioner works by removing heat and moisture from the air inside a building, and then circulating cooled and dehumidified air back into the room. It uses a refrigerant to cool the air, and a fan to circulate it. This helps to maintain a comfortable indoor temperature and humidity level, even during hot and humid weather conditions.

Calculate the specific latent heat of vaporization of steam of 1.13 x 106J pf heat energy is required to convert 15kg of it to water.

Bayanin Amsa

The specific latent heat of vaporization of steam is the amount of heat energy required to convert one kilogram of water into steam at a constant temperature. The given problem states that 1.13 x 106 J of heat energy is required to convert 15 kg of steam to water. We can use the formula: heat energy = mass x specific latent heat where the mass is 15 kg and the heat energy is 1.13 x 106 J. Rearranging the formula, we get: specific latent heat = heat energy / mass Substituting the values, we get: specific latent heat = 1.13 x 106 J / 15 kg = 7.53 x 104 J/kg Therefore, the specific latent heat of vaporization of steam is 7.53 x 104 J/kg. The correct option is (3): 7.53 x 104 J/kg-1.

The volume of a fixed mass of gas is 10cm3 when its pressure is 400cmHg. Determine the volume of the gas when its pressure is 200cmHg.

Bayanin Amsa

This problem can be solved using Boyle's law, which states that the pressure of a gas is inversely proportional to its volume, as long as the temperature remains constant. Mathematically, Boyle's law can be written as: P1V1 = P2V2 where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. In this problem, we are given that the initial volume (V1) is 10cm^3 and the initial pressure (P1) is 400cmHg. We are asked to find the final volume (V2) when the pressure (P2) is 200cmHg. Using Boyle's law, we can write: P1V1 = P2V2 400cmHg x 10cm^3 = 200cmHg x V2 Solving for V2, we get: V2 = (400cmHg x 10cm^3) / 200cmHg V2 = 20cm^3 Therefore, the volume of the gas when its pressure is 200cmHg is 20cm^3. Answer option (D) is correct.

Calculate the upthrust on an object of volume 50cm3 which is immersed in liquid of density 103kgm-3 [g = 10ms-2]

Bayanin Amsa

To calculate the upthrust on an object immersed in a fluid, we need to use Archimedes' principle which states that the upthrust (buoyant force) experienced by an object partially or fully submerged in a fluid is equal to the weight of the fluid displaced by the object. First, let's convert the volume of the object into meters cubed: 50 cm^3 = (50/100)^3 m^3 = 0.0005 m^3 The weight of the liquid displaced by the object is: density of liquid x volume of liquid displaced x acceleration due to gravity = 103 kg/m^3 x 0.0005 m^3 x 10 m/s^2 = 0.515 N Therefore, the upthrust (buoyant force) acting on the object is 0.515 N. So, the correct answer is option C: 0.5N.

I. Refraction II. Interference III. Diffraction Which of the above properties are common to all waves?

Bayanin Amsa

The property that is common to all waves is "I. Refraction". Refraction is the bending of a wave as it passes from one medium to another, and it occurs for all types of waves, including light, sound, and water waves. On the other hand, "II. Interference" and "III. Diffraction" are not common to all waves. Interference is the phenomenon of two waves overlapping and producing a resultant wave with a new amplitude and phase, which occurs only for waves that are capable of superposition, such as light and sound waves. Diffraction is the bending of waves around obstacles or through small openings, which also occurs only for waves with wavelengths comparable to the size of the obstacle or opening, such as light and water waves, but not for sound waves with longer wavelengths.

When the r.m.s value of a source of electricity supply is given as 240v, it means that the peak value of the supply is

Bayanin Amsa

When the r.m.s value of a source of electricity supply is given as 240V, it means that the peak value of the supply is about 340V. The root-mean-square (r.m.s) value of an AC voltage or current is a way to express the effective or average value of that signal. In the case of a sine wave, the r.m.s value is approximately 0.707 times the peak value of the wave. So, to calculate the peak voltage of a 240V r.m.s supply, we can divide the r.m.s value by 0.707. Using this formula, the peak value of a 240V r.m.s supply can be calculated as: Peak value = r.m.s value / 0.707 = 240V / 0.707 ≈ 339.6V Therefore, the peak value of the supply is approximately 340V. It is important to note that this formula assumes a perfect sine wave, and in reality, the peak value of a voltage signal can fluctuate depending on various factors.

Calculate the electric field intensity between two plates of potential difference 6.5V when separated by a distance of 35cm.

Bayanin Amsa

The electric field intensity E between two parallel plates of potential difference V separated by a distance d is given by E = V/d. Substituting the given values, we have E = 6.5V/0.35m = 18.57 NC^−1. Therefore, the electric field intensity between the two plates is 18.57 NC^−1. Answer: 18.57NC^−1

Calculate the time taken for a mango fruit that fall from the tree 20 m to the ground [g = 10 ms-2]

Bayanin Amsa

To calculate the time taken for a mango fruit to fall from a tree to the ground, we can use the following formula: distance = (1/2) x acceleration x time^2 Where: distance = 20m (the height of the tree) acceleration = 10 m/s^2 (acceleration due to gravity) time = unknown (what we are solving for) Rearranging the formula, we get: time = square root(2 x distance / acceleration) Plugging in the values we get: time = square root(2 x 20 / 10) time = square root(4) time = 2 seconds Therefore, the time taken for a mango fruit to fall from a tree 20 m to the ground is 2 seconds.

A block and tackle pulley arrangement has 6 pulleys in which an effort of 50N supports a load of 200N, calculate the efficiency of the machine

Bayanin Amsa

To calculate the efficiency of the block and tackle pulley arrangement, we need to use the formula: efficiency = (load × distance moved by load) / (effort × distance moved by effort) In this case, the load is 200N and the effort is 50N. Since the load is being lifted, its distance moved is equal to the height it is lifted. Let's assume the load is lifted by a distance of 1 meter. Since the effort is being applied over a greater distance due to the pulley system, let's assume it moves a distance of 6 meters (since there are 6 pulleys). Using these values in the formula, we get: efficiency = (200N × 1m) / (50N × 6m) = 0.6667 or 66.67% Therefore, the efficiency of the block and tackle pulley arrangement is 66.67%. This means that only 66.67% of the effort is used to lift the load, with the rest being lost to friction and other factors.

A constant force of 5N acts for 5 seconds on a mass of 5kg initially at rest. Calculate the final momentum

Bayanin Amsa

Impulse = momentum

Impulse = Force (f) × time (t)

Momentum = mass (m) × velocity (v)

? Ft = Final momentum - initial momentum

FT = mv - mu

Since it is initially at rest u = 0

? 5 × 5 = mv ? m(0)

25 = mv

? Final momentum = 25kgms${}^{?1}$

When two objects P and Q are supplied with the same quantity of heat, the temperature change in P is observed to be twice that of Q. The mass of P is half that of Q. The ratio of the specific heat capacity pf P to Q is

Bayanin Amsa

H = mcθ

HP = HQ, θP = 2θ,

mP = $\frac{1}{2}$mQ

∴ HP = mQCPθP, also HQ = mQCQθQ

Since HP = HQ

∴ mPcPθP = mQcPθq

Putting in the conditions

$\frac{1}{2}$mQ × cP × 2θQ = mQ × θQ × cQ

∴ cP = cQ

$\frac{C_p}{C_Q}$= $\frac{1}{1}$

= 1:1

Which of the following statements is NOT correct?

Bayanin Amsa

The correct answer is "Molecules of a liquid are stationary" is not correct. This statement is incorrect because the molecules of a liquid are not stationary, they are in constant motion. The molecules in a liquid are able to move past each other, which is why liquids can take the shape of their container. The other statements are all correct. Matter is indeed made up of molecules, and the constant motion of these molecules is what gives matter its physical properties. Brownian motion, which is the random movement of particles in a fluid, is a visible example of the motion of particles in matter and provides evidence for the particle nature of matter.

The S.I unit of moment of a force is

Bayanin Amsa

Moment of a force is the product of a force and the perpendicular distance from the line of action of the force
Moment = force × distance
= N × m
= Nm